Natural and perturbed dynamics about Trojan bodies

An analysis of the dynamics of a mass-less spacecraft (or point mass) around an in-homogeneousTrojan body in a system composed of three primaries lying at the
vertexes of an equilateral triangle, with their mutual positions fixed over
the course of the motion is here presented. To this end two suitable models
are identified to represent the system, depending on the distance from the
primary. The first model, adopted for use close to the asteroid, where the
dynamics is dominated by this sole body, is the Restricted Two Body Problem.
In this model the in-homogeneities of the asteroid are taken into account as
they have a dominant effect on the dynamics of the spacecraft. The second
model is the Lagrangian Circular Restricted Four Body Problem (CR4BP), which
is adopted far from the asteroid, where the gravitational perturbations of the
Sun and Jupiter are dominant while the in-homogeneities of the asteroid are
negligible.
Low-thrust propulsion perturbations are incorporated into this model. The
possibility to determine the range of validity of each model using an
application of a Weak Stability Boundary (WSB) theory is investigated and
applied.
Applications are shown for the main example of Lagrangian configuration in the
Solar system, the Sun-Jupiter-Trojan-spacecraft system.